Do I need to optimize PNGs after I will output them from Blender and before I will import them to video editing software?
No, assuming by optimize you mean with an optimizer such as pngcrush. These optimizers are designed to strip out extra information in the file in order to reach the smallest acceptable file size, which seems unlikely to matter much for files that will only be used while you're editing your video. If optimizing accomplishes anything, it'll be to optimize away information which might have been useful when making further tweaks in your video editor.

As brockmann pointed out in the comments, using EXR is preferable to PNG, if your video editing software supports it.